"I can reassure you that the coalition is stable", he said.
"Someone with such serious accusations against them, many of which he does not even deny, can not continue to serve as prime minister with responsibility for the security and well-being of Israel's citizens, " Lapid said.
The police announcement that Netanyahu's acceptance of almost $300,000 in gifts from two billionaires amounted to bribery sent shockwaves through the Israeli political system and delivered a humiliating blow to Netanyahu after years of allegations and investigations.
The case now goes to Attorney General Avihai Mandelblit for review, before he decides whether to file charges. Despite police recommendations, Netanyahu does not need to resign from his position.
"Over the years, I have been the subject of at least 15 inquiries and investigations", he said.
Netanyahu, who seemed to expect police announcement since last week, denied being bribed and announced he will remain in office.
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The second, Case 2000, also alleged "bribery, fraud and breach of trust by the prime minister" and by the publisher of the biggest-selling Israeli newspaper Yedioth Ahronoth, Arnon Mozes. "I am certain, as I have always been certain, and nothing has changed, that the truth will come to light and nothing will come of this".
Mr Milchan, the producer of films including Fight Club, Gone Girl and The Revenant, should face bribery charges, police said.
Ofer Shelah, a lawmaker with the opposition Yesh Atid party, says criticism of his party's leader Yair Lapid - a key witness in the case against Netanyahu - is "an attempt to divert the conversation from what happened". His Likud allies lashed out at Lapid, with Amsalem angrily calling him a "snitch". According to Lapid, Netanyahu should resign because "there is no way to run a state under such serious allegations". Netanyahu was Prime Minister of Israel from 1996 to 1999 and resumed his post in 2009. Not in a single day, not in a year, not at all, " Hadad said.
In his television appearance, minutes after police made their recommendations public, Netanyahu, 68, recounted his military service as a commando and said he had never sought personal gain from politics.
Lapid had not agreed to the "Milchan Law" but Netanyahu allegedly told him that the law has to be passed.
A public debate has always been under way in Israel on whether Mandelblit, who has avoided interviews, might be reluctant to prosecute a sitting prime minister for the first time in Israeli history, especially one who has promoted his career. "The prime minister must show national responsibility - you can not be prime minister, foreign minister and health minister, while you spend most of your time with lawyers and dealing with media reactions".
During similar circumstances a decade ago, Netanyahu, as opposition leader, urged then-Prime Minister Ehud Olmert to resign during a police investigation, saying a leader "sunk up to his neck in interrogations" could not govern properly.